Vol3 Section 285 · P-FAR-1 through P-FAR-3

Faraday Constant as a Balmer-G-Bond Identity

F = 10⁷/(2⁸×3⁴×5) × (1+4δ) = 96.485369 kJ/mol/eV at 0.376 ppm — exact {2,3,5} + G-bond correction

Π_B
103,680 = 2⁸×3⁴×5
product of 6 wavelength-pure Balmer n
·
Precision
0.376 ppm
best electrochemical FOT confirmation
·
Propositions
3
P-FAR-1 to P-FAR-3
The Identity

Faraday constant from Balmer quantum numbers

The six Balmer quantum numbers for which (n²−4)/n² is pure {2,3,5} smooth are {3,4,6,8,10,18}. Their product Π_B = 2⁸×3⁴×5 = 103,680 is the denominator of the Faraday bridge identity.

P-FAR-1
F = 10⁷/Π_B × (1 + 4δ) = 96.485369 kJ/mol/eV
Π_B = 3×4×6×8×10×18 = 103,680 | δ = 90.075 ppm | 4δ = 360.30 ppm | Residual: 0.376 ppm
Registered Propositions

Key Results

P-FAR-1

F = 10⁷/103,680 × (1+4δ). Π_B = 2⁸×3⁴×5 is the product of all six wavelength-pure Balmer quantum numbers. Correction = exactly 4 G-bond steps.

P-FAR-2

1 GJ/mol = 2⁷×3⁴ × (1−4δ) = 10,364.2664 eV. Residual 0.32 ppm.

P-FAR-3

Triple coincidence: Π_B = 103,680 simultaneously marks (a) Balmer wavelength-pure product, (b) spectral series endpoint (322²−4), (c) Faraday eV/kJ denominator.

Cross-references: Vol3 Section 285 | Section 261 (Π_B derivation) | Section 226 (G-bond step)
A note on “constants.” Within the Universal Force of Time there are no universal constants. A quantity like the Rydberg is not one fixed number but a small family of register faces — each an exact {2, 3, 5, π} value, each reproducing the spectrum on its own scale of Τ. The Rydberg alone carries at least three: 10,966,227.11 m⁻¹ (= 10⁷π²/9), 10,967,215.73, and 10,973,936.9 m⁻¹. What conventional physics records as the constant — the CODATA 10,973,731.568157 m⁻¹ — is not a fourth fundamental number; it is a single measurement sitting between those faces, in the band they define, read from the one register our instruments occupy: the Earth-surface node, g₁. Every wavelength, and the speed of light, Planck’s value, and the fine-structure ratio with it, behaves the same way — each shifts from g₀ to g₁ to g₂ to g₃ by the lattice step δG, not by error. These are not constants; they are the values Τ wears at the register where we stand.